Properties

Label 120.2.m.b.59.3
Level $120$
Weight $2$
Character 120.59
Analytic conductor $0.958$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.m (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.958204824255\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 24x^{14} + 192x^{12} + 672x^{10} + 1092x^{8} + 880x^{6} + 352x^{4} + 64x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 59.3
Root \(-1.05636i\) of defining polynomial
Character \(\chi\) \(=\) 120.59
Dual form 120.2.m.b.59.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.30656 + 0.541196i) q^{2} +(0.541196 - 1.64533i) q^{3} +(1.41421 - 1.41421i) q^{4} +(-1.25928 - 1.84776i) q^{5} +(0.183339 + 2.44262i) q^{6} -3.29066 q^{7} +(-1.08239 + 2.61313i) q^{8} +(-2.41421 - 1.78089i) q^{9} +O(q^{10})\) \(q+(-1.30656 + 0.541196i) q^{2} +(0.541196 - 1.64533i) q^{3} +(1.41421 - 1.41421i) q^{4} +(-1.25928 - 1.84776i) q^{5} +(0.183339 + 2.44262i) q^{6} -3.29066 q^{7} +(-1.08239 + 2.61313i) q^{8} +(-2.41421 - 1.78089i) q^{9} +(2.64533 + 1.73270i) q^{10} -2.51856i q^{11} +(-1.56148 - 3.09221i) q^{12} +4.65369 q^{13} +(4.29945 - 1.78089i) q^{14} +(-3.72169 + 1.07193i) q^{15} -4.00000i q^{16} +3.69552 q^{17} +(4.11813 + 1.02028i) q^{18} +0.828427 q^{19} +(-4.39402 - 0.832235i) q^{20} +(-1.78089 + 5.41421i) q^{21} +(1.36303 + 3.29066i) q^{22} -2.61313i q^{23} +(3.71366 + 3.19510i) q^{24} +(-1.82843 + 4.65369i) q^{25} +(-6.08034 + 2.51856i) q^{26} +(-4.23671 + 3.00836i) q^{27} +(-4.65369 + 4.65369i) q^{28} +6.08034 q^{29} +(4.28250 - 3.41471i) q^{30} -1.17157i q^{31} +(2.16478 + 5.22625i) q^{32} +(-4.14386 - 1.36303i) q^{33} +(-4.82843 + 2.00000i) q^{34} +(4.14386 + 6.08034i) q^{35} +(-5.93277 + 0.895653i) q^{36} +1.92762 q^{37} +(-1.08239 + 0.448342i) q^{38} +(2.51856 - 7.65685i) q^{39} +(6.19146 - 1.29066i) q^{40} +8.59890i q^{41} +(-0.603305 - 8.03782i) q^{42} -6.01673i q^{43} +(-3.56178 - 3.56178i) q^{44} +(-0.250486 + 6.70353i) q^{45} +(1.41421 + 3.41421i) q^{46} +2.61313i q^{47} +(-6.58132 - 2.16478i) q^{48} +3.82843 q^{49} +(-0.129605 - 7.06988i) q^{50} +(2.00000 - 6.08034i) q^{51} +(6.58132 - 6.58132i) q^{52} -4.59220i q^{53} +(3.90742 - 6.22351i) q^{54} +(-4.65369 + 3.17157i) q^{55} +(3.56178 - 8.59890i) q^{56} +(0.448342 - 1.36303i) q^{57} +(-7.94435 + 3.29066i) q^{58} +2.51856i q^{59} +(-3.74732 + 6.77920i) q^{60} -8.48528i q^{61} +(0.634051 + 1.53073i) q^{62} +(7.94435 + 5.86030i) q^{63} +(-5.65685 - 5.65685i) q^{64} +(-5.86030 - 8.59890i) q^{65} +(6.15188 - 0.461750i) q^{66} +3.29066i q^{67} +(5.22625 - 5.22625i) q^{68} +(-4.29945 - 1.41421i) q^{69} +(-8.70487 - 5.70171i) q^{70} +7.12356 q^{71} +(7.26682 - 4.38102i) q^{72} -6.58132i q^{73} +(-2.51856 + 1.04322i) q^{74} +(6.66732 + 5.52692i) q^{75} +(1.17157 - 1.17157i) q^{76} +8.28772i q^{77} +(0.853202 + 11.3672i) q^{78} +16.4853i q^{79} +(-7.39104 + 5.03712i) q^{80} +(2.65685 + 8.59890i) q^{81} +(-4.65369 - 11.2350i) q^{82} -9.37011 q^{83} +(5.13829 + 10.1754i) q^{84} +(-4.65369 - 6.82843i) q^{85} +(3.25623 + 7.86123i) q^{86} +(3.29066 - 10.0042i) q^{87} +(6.58132 + 2.72607i) q^{88} -5.03712i q^{89} +(-3.30065 - 8.89414i) q^{90} -15.3137 q^{91} +(-3.69552 - 3.69552i) q^{92} +(-1.92762 - 0.634051i) q^{93} +(-1.41421 - 3.41421i) q^{94} +(-1.04322 - 1.53073i) q^{95} +(9.77048 - 0.733355i) q^{96} +2.72607i q^{97} +(-5.00208 + 2.07193i) q^{98} +(-4.48528 + 6.08034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{9} + 16 q^{10} - 32 q^{19} - 32 q^{24} + 16 q^{25} + 16 q^{30} - 32 q^{34} - 32 q^{36} + 32 q^{40} + 16 q^{49} + 32 q^{51} + 32 q^{54} + 64 q^{66} - 64 q^{70} + 32 q^{75} + 64 q^{76} - 48 q^{81} + 32 q^{84} - 16 q^{90} - 64 q^{91} + 64 q^{96} + 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.30656 + 0.541196i −0.923880 + 0.382683i
\(3\) 0.541196 1.64533i 0.312460 0.949931i
\(4\) 1.41421 1.41421i 0.707107 0.707107i
\(5\) −1.25928 1.84776i −0.563167 0.826343i
\(6\) 0.183339 + 2.44262i 0.0748477 + 0.997195i
\(7\) −3.29066 −1.24375 −0.621876 0.783116i \(-0.713629\pi\)
−0.621876 + 0.783116i \(0.713629\pi\)
\(8\) −1.08239 + 2.61313i −0.382683 + 0.923880i
\(9\) −2.41421 1.78089i −0.804738 0.593630i
\(10\) 2.64533 + 1.73270i 0.836526 + 0.547927i
\(11\) 2.51856i 0.759374i −0.925115 0.379687i \(-0.876032\pi\)
0.925115 0.379687i \(-0.123968\pi\)
\(12\) −1.56148 3.09221i −0.450760 0.892645i
\(13\) 4.65369 1.29070 0.645351 0.763886i \(-0.276711\pi\)
0.645351 + 0.763886i \(0.276711\pi\)
\(14\) 4.29945 1.78089i 1.14908 0.475963i
\(15\) −3.72169 + 1.07193i −0.960936 + 0.276771i
\(16\) 4.00000i 1.00000i
\(17\) 3.69552 0.896295 0.448147 0.893960i \(-0.352084\pi\)
0.448147 + 0.893960i \(0.352084\pi\)
\(18\) 4.11813 + 1.02028i 0.970653 + 0.240483i
\(19\) 0.828427 0.190054 0.0950271 0.995475i \(-0.469706\pi\)
0.0950271 + 0.995475i \(0.469706\pi\)
\(20\) −4.39402 0.832235i −0.982532 0.186093i
\(21\) −1.78089 + 5.41421i −0.388622 + 1.18148i
\(22\) 1.36303 + 3.29066i 0.290600 + 0.701571i
\(23\) 2.61313i 0.544874i −0.962174 0.272437i \(-0.912170\pi\)
0.962174 0.272437i \(-0.0878297\pi\)
\(24\) 3.71366 + 3.19510i 0.758049 + 0.652198i
\(25\) −1.82843 + 4.65369i −0.365685 + 0.930739i
\(26\) −6.08034 + 2.51856i −1.19245 + 0.493930i
\(27\) −4.23671 + 3.00836i −0.815356 + 0.578960i
\(28\) −4.65369 + 4.65369i −0.879465 + 0.879465i
\(29\) 6.08034 1.12909 0.564546 0.825402i \(-0.309051\pi\)
0.564546 + 0.825402i \(0.309051\pi\)
\(30\) 4.28250 3.41471i 0.781873 0.623437i
\(31\) 1.17157i 0.210421i −0.994450 0.105210i \(-0.966448\pi\)
0.994450 0.105210i \(-0.0335516\pi\)
\(32\) 2.16478 + 5.22625i 0.382683 + 0.923880i
\(33\) −4.14386 1.36303i −0.721353 0.237274i
\(34\) −4.82843 + 2.00000i −0.828068 + 0.342997i
\(35\) 4.14386 + 6.08034i 0.700440 + 1.02777i
\(36\) −5.93277 + 0.895653i −0.988796 + 0.149276i
\(37\) 1.92762 0.316899 0.158450 0.987367i \(-0.449350\pi\)
0.158450 + 0.987367i \(0.449350\pi\)
\(38\) −1.08239 + 0.448342i −0.175587 + 0.0727306i
\(39\) 2.51856 7.65685i 0.403292 1.22608i
\(40\) 6.19146 1.29066i 0.978956 0.204071i
\(41\) 8.59890i 1.34292i 0.741039 + 0.671461i \(0.234333\pi\)
−0.741039 + 0.671461i \(0.765667\pi\)
\(42\) −0.603305 8.03782i −0.0930920 1.24026i
\(43\) 6.01673i 0.917542i −0.888554 0.458771i \(-0.848290\pi\)
0.888554 0.458771i \(-0.151710\pi\)
\(44\) −3.56178 3.56178i −0.536959 0.536959i
\(45\) −0.250486 + 6.70353i −0.0373403 + 0.999303i
\(46\) 1.41421 + 3.41421i 0.208514 + 0.503398i
\(47\) 2.61313i 0.381164i 0.981671 + 0.190582i \(0.0610374\pi\)
−0.981671 + 0.190582i \(0.938963\pi\)
\(48\) −6.58132 2.16478i −0.949931 0.312460i
\(49\) 3.82843 0.546918
\(50\) −0.129605 7.06988i −0.0183289 0.999832i
\(51\) 2.00000 6.08034i 0.280056 0.851418i
\(52\) 6.58132 6.58132i 0.912664 0.912664i
\(53\) 4.59220i 0.630787i −0.948961 0.315394i \(-0.897863\pi\)
0.948961 0.315394i \(-0.102137\pi\)
\(54\) 3.90742 6.22351i 0.531732 0.846912i
\(55\) −4.65369 + 3.17157i −0.627504 + 0.427655i
\(56\) 3.56178 8.59890i 0.475963 1.14908i
\(57\) 0.448342 1.36303i 0.0593843 0.180538i
\(58\) −7.94435 + 3.29066i −1.04314 + 0.432085i
\(59\) 2.51856i 0.327889i 0.986470 + 0.163944i \(0.0524217\pi\)
−0.986470 + 0.163944i \(0.947578\pi\)
\(60\) −3.74732 + 6.77920i −0.483778 + 0.875191i
\(61\) 8.48528i 1.08643i −0.839594 0.543214i \(-0.817207\pi\)
0.839594 0.543214i \(-0.182793\pi\)
\(62\) 0.634051 + 1.53073i 0.0805245 + 0.194403i
\(63\) 7.94435 + 5.86030i 1.00089 + 0.738329i
\(64\) −5.65685 5.65685i −0.707107 0.707107i
\(65\) −5.86030 8.59890i −0.726881 1.06656i
\(66\) 6.15188 0.461750i 0.757244 0.0568375i
\(67\) 3.29066i 0.402018i 0.979589 + 0.201009i \(0.0644220\pi\)
−0.979589 + 0.201009i \(0.935578\pi\)
\(68\) 5.22625 5.22625i 0.633776 0.633776i
\(69\) −4.29945 1.41421i −0.517593 0.170251i
\(70\) −8.70487 5.70171i −1.04043 0.681485i
\(71\) 7.12356 0.845412 0.422706 0.906267i \(-0.361080\pi\)
0.422706 + 0.906267i \(0.361080\pi\)
\(72\) 7.26682 4.38102i 0.856403 0.516308i
\(73\) 6.58132i 0.770285i −0.922857 0.385142i \(-0.874152\pi\)
0.922857 0.385142i \(-0.125848\pi\)
\(74\) −2.51856 + 1.04322i −0.292777 + 0.121272i
\(75\) 6.66732 + 5.52692i 0.769875 + 0.638194i
\(76\) 1.17157 1.17157i 0.134389 0.134389i
\(77\) 8.28772i 0.944473i
\(78\) 0.853202 + 11.3672i 0.0966061 + 1.28708i
\(79\) 16.4853i 1.85474i 0.374147 + 0.927370i \(0.377936\pi\)
−0.374147 + 0.927370i \(0.622064\pi\)
\(80\) −7.39104 + 5.03712i −0.826343 + 0.563167i
\(81\) 2.65685 + 8.59890i 0.295206 + 0.955434i
\(82\) −4.65369 11.2350i −0.513914 1.24070i
\(83\) −9.37011 −1.02850 −0.514252 0.857639i \(-0.671930\pi\)
−0.514252 + 0.857639i \(0.671930\pi\)
\(84\) 5.13829 + 10.1754i 0.560634 + 1.11023i
\(85\) −4.65369 6.82843i −0.504764 0.740647i
\(86\) 3.25623 + 7.86123i 0.351128 + 0.847699i
\(87\) 3.29066 10.0042i 0.352796 1.07256i
\(88\) 6.58132 + 2.72607i 0.701571 + 0.290600i
\(89\) 5.03712i 0.533934i −0.963706 0.266967i \(-0.913979\pi\)
0.963706 0.266967i \(-0.0860214\pi\)
\(90\) −3.30065 8.89414i −0.347919 0.937525i
\(91\) −15.3137 −1.60531
\(92\) −3.69552 3.69552i −0.385284 0.385284i
\(93\) −1.92762 0.634051i −0.199885 0.0657480i
\(94\) −1.41421 3.41421i −0.145865 0.352149i
\(95\) −1.04322 1.53073i −0.107032 0.157050i
\(96\) 9.77048 0.733355i 0.997195 0.0748477i
\(97\) 2.72607i 0.276790i 0.990377 + 0.138395i \(0.0441944\pi\)
−0.990377 + 0.138395i \(0.955806\pi\)
\(98\) −5.00208 + 2.07193i −0.505286 + 0.209297i
\(99\) −4.48528 + 6.08034i −0.450788 + 0.611097i
\(100\) 3.99553 + 9.16710i 0.399553 + 0.916710i
\(101\) −13.2039 −1.31384 −0.656919 0.753961i \(-0.728141\pi\)
−0.656919 + 0.753961i \(0.728141\pi\)
\(102\) 0.677532 + 9.02674i 0.0670856 + 0.893781i
\(103\) 6.01673 0.592846 0.296423 0.955057i \(-0.404206\pi\)
0.296423 + 0.955057i \(0.404206\pi\)
\(104\) −5.03712 + 12.1607i −0.493930 + 1.19245i
\(105\) 12.2468 3.52735i 1.19517 0.344235i
\(106\) 2.48528 + 6.00000i 0.241392 + 0.582772i
\(107\) 8.47343 0.819157 0.409579 0.912275i \(-0.365676\pi\)
0.409579 + 0.912275i \(0.365676\pi\)
\(108\) −1.73715 + 10.2461i −0.167157 + 0.985930i
\(109\) 0.485281i 0.0464815i 0.999730 + 0.0232408i \(0.00739843\pi\)
−0.999730 + 0.0232408i \(0.992602\pi\)
\(110\) 4.36390 6.66242i 0.416081 0.635237i
\(111\) 1.04322 3.17157i 0.0990182 0.301032i
\(112\) 13.1626i 1.24375i
\(113\) 8.92177 0.839290 0.419645 0.907688i \(-0.362155\pi\)
0.419645 + 0.907688i \(0.362155\pi\)
\(114\) 0.151883 + 2.02353i 0.0142251 + 0.189521i
\(115\) −4.82843 + 3.29066i −0.450253 + 0.306855i
\(116\) 8.59890 8.59890i 0.798388 0.798388i
\(117\) −11.2350 8.28772i −1.03868 0.766200i
\(118\) −1.36303 3.29066i −0.125478 0.302930i
\(119\) −12.1607 −1.11477
\(120\) 1.22724 10.8855i 0.112031 0.993705i
\(121\) 4.65685 0.423350
\(122\) 4.59220 + 11.0866i 0.415758 + 1.00373i
\(123\) 14.1480 + 4.65369i 1.27568 + 0.419609i
\(124\) −1.65685 1.65685i −0.148790 0.148790i
\(125\) 10.9014 2.48181i 0.975051 0.221980i
\(126\) −13.5514 3.35740i −1.20725 0.299101i
\(127\) 3.29066 0.291999 0.145999 0.989285i \(-0.453360\pi\)
0.145999 + 0.989285i \(0.453360\pi\)
\(128\) 10.4525 + 4.32957i 0.923880 + 0.382683i
\(129\) −9.89949 3.25623i −0.871602 0.286695i
\(130\) 12.3105 + 8.06343i 1.07971 + 0.707210i
\(131\) 21.8028i 1.90492i −0.304663 0.952460i \(-0.598544\pi\)
0.304663 0.952460i \(-0.401456\pi\)
\(132\) −7.78793 + 3.93268i −0.677852 + 0.342296i
\(133\) −2.72607 −0.236380
\(134\) −1.78089 4.29945i −0.153846 0.371416i
\(135\) 10.8939 + 4.04005i 0.937601 + 0.347713i
\(136\) −4.00000 + 9.65685i −0.342997 + 0.828068i
\(137\) −11.9832 −1.02380 −0.511899 0.859046i \(-0.671058\pi\)
−0.511899 + 0.859046i \(0.671058\pi\)
\(138\) 6.38287 0.479087i 0.543346 0.0407826i
\(139\) 14.4853 1.22863 0.614313 0.789063i \(-0.289433\pi\)
0.614313 + 0.789063i \(0.289433\pi\)
\(140\) 14.4592 + 2.73860i 1.22203 + 0.231454i
\(141\) 4.29945 + 1.41421i 0.362079 + 0.119098i
\(142\) −9.30739 + 3.85525i −0.781058 + 0.323525i
\(143\) 11.7206i 0.980126i
\(144\) −7.12356 + 9.65685i −0.593630 + 0.804738i
\(145\) −7.65685 11.2350i −0.635867 0.933017i
\(146\) 3.56178 + 8.59890i 0.294775 + 0.711650i
\(147\) 2.07193 6.29902i 0.170890 0.519535i
\(148\) 2.72607 2.72607i 0.224082 0.224082i
\(149\) −14.6792 −1.20257 −0.601285 0.799034i \(-0.705344\pi\)
−0.601285 + 0.799034i \(0.705344\pi\)
\(150\) −11.7024 3.61295i −0.955498 0.294996i
\(151\) 2.82843i 0.230174i 0.993355 + 0.115087i \(0.0367147\pi\)
−0.993355 + 0.115087i \(0.963285\pi\)
\(152\) −0.896683 + 2.16478i −0.0727306 + 0.175587i
\(153\) −8.92177 6.58132i −0.721282 0.532068i
\(154\) −4.48528 10.8284i −0.361434 0.872580i
\(155\) −2.16478 + 1.47534i −0.173880 + 0.118502i
\(156\) −7.26665 14.3902i −0.581797 1.15214i
\(157\) −5.78287 −0.461523 −0.230762 0.973010i \(-0.574122\pi\)
−0.230762 + 0.973010i \(0.574122\pi\)
\(158\) −8.92177 21.5391i −0.709778 1.71356i
\(159\) −7.55568 2.48528i −0.599204 0.197096i
\(160\) 6.93078 10.5813i 0.547927 0.836526i
\(161\) 8.59890i 0.677688i
\(162\) −8.12504 9.79713i −0.638363 0.769735i
\(163\) 6.01673i 0.471266i 0.971842 + 0.235633i \(0.0757164\pi\)
−0.971842 + 0.235633i \(0.924284\pi\)
\(164\) 12.1607 + 12.1607i 0.949590 + 0.949590i
\(165\) 2.69972 + 9.37330i 0.210173 + 0.729710i
\(166\) 12.2426 5.07107i 0.950213 0.393591i
\(167\) 17.3952i 1.34608i 0.739606 + 0.673040i \(0.235012\pi\)
−0.739606 + 0.673040i \(0.764988\pi\)
\(168\) −12.2204 10.5140i −0.942824 0.811172i
\(169\) 8.65685 0.665912
\(170\) 9.77586 + 6.40321i 0.749774 + 0.491104i
\(171\) −2.00000 1.47534i −0.152944 0.112822i
\(172\) −8.50894 8.50894i −0.648800 0.648800i
\(173\) 21.5391i 1.63758i 0.574090 + 0.818792i \(0.305356\pi\)
−0.574090 + 0.818792i \(0.694644\pi\)
\(174\) 1.11476 + 14.8520i 0.0845099 + 1.12592i
\(175\) 6.01673 15.3137i 0.454822 1.15761i
\(176\) −10.0742 −0.759374
\(177\) 4.14386 + 1.36303i 0.311472 + 0.102452i
\(178\) 2.72607 + 6.58132i 0.204328 + 0.493290i
\(179\) 9.64212i 0.720686i 0.932820 + 0.360343i \(0.117340\pi\)
−0.932820 + 0.360343i \(0.882660\pi\)
\(180\) 9.12598 + 9.83446i 0.680210 + 0.733017i
\(181\) 10.3431i 0.768800i 0.923167 + 0.384400i \(0.125592\pi\)
−0.923167 + 0.384400i \(0.874408\pi\)
\(182\) 20.0083 8.28772i 1.48312 0.614327i
\(183\) −13.9611 4.59220i −1.03203 0.339465i
\(184\) 6.82843 + 2.82843i 0.503398 + 0.208514i
\(185\) −2.42742 3.56178i −0.178467 0.261867i
\(186\) 2.86171 0.214795i 0.209830 0.0157495i
\(187\) 9.30739i 0.680623i
\(188\) 3.69552 + 3.69552i 0.269523 + 0.269523i
\(189\) 13.9416 9.89949i 1.01410 0.720082i
\(190\) 2.19146 + 1.43541i 0.158985 + 0.104136i
\(191\) 5.03712 0.364473 0.182237 0.983255i \(-0.441666\pi\)
0.182237 + 0.983255i \(0.441666\pi\)
\(192\) −12.3689 + 6.24592i −0.892645 + 0.450760i
\(193\) 19.7439i 1.42120i 0.703596 + 0.710600i \(0.251576\pi\)
−0.703596 + 0.710600i \(0.748424\pi\)
\(194\) −1.47534 3.56178i −0.105923 0.255721i
\(195\) −17.3196 + 4.98843i −1.24028 + 0.357229i
\(196\) 5.41421 5.41421i 0.386730 0.386730i
\(197\) 11.9832i 0.853770i −0.904306 0.426885i \(-0.859611\pi\)
0.904306 0.426885i \(-0.140389\pi\)
\(198\) 2.56964 10.3718i 0.182617 0.737089i
\(199\) 9.17157i 0.650156i −0.945687 0.325078i \(-0.894610\pi\)
0.945687 0.325078i \(-0.105390\pi\)
\(200\) −10.1816 9.81503i −0.719949 0.694027i
\(201\) 5.41421 + 1.78089i 0.381889 + 0.125614i
\(202\) 17.2517 7.14590i 1.21383 0.502784i
\(203\) −20.0083 −1.40431
\(204\) −5.77048 11.4273i −0.404014 0.800073i
\(205\) 15.8887 10.8284i 1.10971 0.756290i
\(206\) −7.86123 + 3.25623i −0.547718 + 0.226872i
\(207\) −4.65369 + 6.30864i −0.323454 + 0.438481i
\(208\) 18.6148i 1.29070i
\(209\) 2.08644i 0.144322i
\(210\) −14.0922 + 11.2366i −0.972456 + 0.775401i
\(211\) 18.4853 1.27258 0.636290 0.771450i \(-0.280468\pi\)
0.636290 + 0.771450i \(0.280468\pi\)
\(212\) −6.49435 6.49435i −0.446034 0.446034i
\(213\) 3.85525 11.7206i 0.264157 0.803083i
\(214\) −11.0711 + 4.58579i −0.756803 + 0.313478i
\(215\) −11.1175 + 7.57675i −0.758205 + 0.516730i
\(216\) −3.27545 14.3273i −0.222866 0.974849i
\(217\) 3.85525i 0.261711i
\(218\) −0.262632 0.634051i −0.0177877 0.0429433i
\(219\) −10.8284 3.56178i −0.731717 0.240683i
\(220\) −2.09603 + 11.0666i −0.141315 + 0.746110i
\(221\) 17.1978 1.15685
\(222\) 0.353408 + 4.70845i 0.0237192 + 0.316010i
\(223\) −21.9054 −1.46690 −0.733448 0.679746i \(-0.762090\pi\)
−0.733448 + 0.679746i \(0.762090\pi\)
\(224\) −7.12356 17.1978i −0.475963 1.14908i
\(225\) 12.7019 7.97878i 0.846796 0.531919i
\(226\) −11.6569 + 4.82843i −0.775402 + 0.321182i
\(227\) 4.14386 0.275038 0.137519 0.990499i \(-0.456087\pi\)
0.137519 + 0.990499i \(0.456087\pi\)
\(228\) −1.29357 2.56167i −0.0856689 0.169651i
\(229\) 19.3137i 1.27629i 0.769918 + 0.638143i \(0.220297\pi\)
−0.769918 + 0.638143i \(0.779703\pi\)
\(230\) 4.52775 6.91258i 0.298551 0.455802i
\(231\) 13.6360 + 4.48528i 0.897184 + 0.295110i
\(232\) −6.58132 + 15.8887i −0.432085 + 1.04314i
\(233\) 15.9414 1.04436 0.522178 0.852837i \(-0.325120\pi\)
0.522178 + 0.852837i \(0.325120\pi\)
\(234\) 19.1645 + 4.74808i 1.25282 + 0.310392i
\(235\) 4.82843 3.29066i 0.314972 0.214659i
\(236\) 3.56178 + 3.56178i 0.231852 + 0.231852i
\(237\) 27.1237 + 8.92177i 1.76187 + 0.579531i
\(238\) 15.8887 6.58132i 1.02991 0.426603i
\(239\) 22.2349 1.43826 0.719129 0.694877i \(-0.244541\pi\)
0.719129 + 0.694877i \(0.244541\pi\)
\(240\) 4.28772 + 14.8868i 0.276771 + 0.960936i
\(241\) −6.48528 −0.417754 −0.208877 0.977942i \(-0.566981\pi\)
−0.208877 + 0.977942i \(0.566981\pi\)
\(242\) −6.08447 + 2.52027i −0.391125 + 0.162009i
\(243\) 15.5859 + 0.282294i 0.999836 + 0.0181092i
\(244\) −12.0000 12.0000i −0.768221 0.768221i
\(245\) −4.82106 7.07401i −0.308006 0.451942i
\(246\) −21.0038 + 1.57651i −1.33916 + 0.100515i
\(247\) 3.85525 0.245303
\(248\) 3.06147 + 1.26810i 0.194403 + 0.0805245i
\(249\) −5.07107 + 15.4169i −0.321366 + 0.977007i
\(250\) −12.9002 + 9.14244i −0.815882 + 0.578219i
\(251\) 11.7286i 0.740301i 0.928972 + 0.370150i \(0.120694\pi\)
−0.928972 + 0.370150i \(0.879306\pi\)
\(252\) 19.5227 2.94729i 1.22982 0.185662i
\(253\) −6.58132 −0.413764
\(254\) −4.29945 + 1.78089i −0.269772 + 0.111743i
\(255\) −13.7536 + 3.96134i −0.861282 + 0.248068i
\(256\) −16.0000 −1.00000
\(257\) −16.3128 −1.01756 −0.508782 0.860895i \(-0.669904\pi\)
−0.508782 + 0.860895i \(0.669904\pi\)
\(258\) 14.6966 1.10310i 0.914969 0.0686760i
\(259\) −6.34315 −0.394144
\(260\) −20.4484 3.87297i −1.26816 0.240191i
\(261\) −14.6792 10.8284i −0.908622 0.670263i
\(262\) 11.7996 + 28.4867i 0.728981 + 1.75992i
\(263\) 22.2500i 1.37200i 0.727604 + 0.685998i \(0.240634\pi\)
−0.727604 + 0.685998i \(0.759366\pi\)
\(264\) 8.04706 9.35309i 0.495263 0.575643i
\(265\) −8.48528 + 5.78287i −0.521247 + 0.355239i
\(266\) 3.56178 1.47534i 0.218387 0.0904588i
\(267\) −8.28772 2.72607i −0.507200 0.166833i
\(268\) 4.65369 + 4.65369i 0.284270 + 0.284270i
\(269\) 9.64212 0.587891 0.293945 0.955822i \(-0.405032\pi\)
0.293945 + 0.955822i \(0.405032\pi\)
\(270\) −16.4201 + 0.617173i −0.999294 + 0.0375600i
\(271\) 14.1421i 0.859074i −0.903049 0.429537i \(-0.858677\pi\)
0.903049 0.429537i \(-0.141323\pi\)
\(272\) 14.7821i 0.896295i
\(273\) −8.28772 + 25.1961i −0.501596 + 1.52494i
\(274\) 15.6569 6.48528i 0.945865 0.391790i
\(275\) 11.7206 + 4.60500i 0.706779 + 0.277692i
\(276\) −8.08034 + 4.08034i −0.486379 + 0.245608i
\(277\) 15.0903 0.906685 0.453343 0.891336i \(-0.350231\pi\)
0.453343 + 0.891336i \(0.350231\pi\)
\(278\) −18.9259 + 7.83938i −1.13510 + 0.470175i
\(279\) −2.08644 + 2.82843i −0.124912 + 0.169334i
\(280\) −20.3740 + 4.24711i −1.21758 + 0.253813i
\(281\) 3.56178i 0.212478i −0.994341 0.106239i \(-0.966119\pi\)
0.994341 0.106239i \(-0.0338809\pi\)
\(282\) −6.38287 + 0.479087i −0.380094 + 0.0285292i
\(283\) 18.0502i 1.07297i 0.843909 + 0.536486i \(0.180249\pi\)
−0.843909 + 0.536486i \(0.819751\pi\)
\(284\) 10.0742 10.0742i 0.597796 0.597796i
\(285\) −3.08315 + 0.888016i −0.182630 + 0.0526015i
\(286\) 6.34315 + 15.3137i 0.375078 + 0.905519i
\(287\) 28.2960i 1.67026i
\(288\) 4.08113 16.4725i 0.240483 0.970653i
\(289\) −3.34315 −0.196656
\(290\) 16.0845 + 10.5354i 0.944515 + 0.618659i
\(291\) 4.48528 + 1.47534i 0.262932 + 0.0864859i
\(292\) −9.30739 9.30739i −0.544674 0.544674i
\(293\) 2.42742i 0.141811i −0.997483 0.0709056i \(-0.977411\pi\)
0.997483 0.0709056i \(-0.0225889\pi\)
\(294\) 0.701899 + 9.35139i 0.0409356 + 0.545384i
\(295\) 4.65369 3.17157i 0.270948 0.184656i
\(296\) −2.08644 + 5.03712i −0.121272 + 0.292777i
\(297\) 7.57675 + 10.6704i 0.439647 + 0.619161i
\(298\) 19.1794 7.94435i 1.11103 0.460204i
\(299\) 12.1607i 0.703271i
\(300\) 17.2453 1.61276i 0.995656 0.0931127i
\(301\) 19.7990i 1.14119i
\(302\) −1.53073 3.69552i −0.0880838 0.212653i
\(303\) −7.14590 + 21.7248i −0.410521 + 1.24806i
\(304\) 3.31371i 0.190054i
\(305\) −15.6788 + 10.6853i −0.897763 + 0.611841i
\(306\) 15.2186 + 3.77048i 0.869992 + 0.215544i
\(307\) 7.14590i 0.407838i −0.978988 0.203919i \(-0.934632\pi\)
0.978988 0.203919i \(-0.0653680\pi\)
\(308\) 11.7206 + 11.7206i 0.667843 + 0.667843i
\(309\) 3.25623 9.89949i 0.185240 0.563163i
\(310\) 2.02998 3.09920i 0.115295 0.176022i
\(311\) −34.3956 −1.95040 −0.975198 0.221334i \(-0.928959\pi\)
−0.975198 + 0.221334i \(0.928959\pi\)
\(312\) 17.2823 + 14.8690i 0.978415 + 0.841793i
\(313\) 17.0179i 0.961907i −0.876746 0.480954i \(-0.840291\pi\)
0.876746 0.480954i \(-0.159709\pi\)
\(314\) 7.55568 3.12967i 0.426392 0.176617i
\(315\) 0.824265 22.0590i 0.0464421 1.24288i
\(316\) 23.3137 + 23.3137i 1.31150 + 1.31150i
\(317\) 13.2513i 0.744269i −0.928179 0.372135i \(-0.878626\pi\)
0.928179 0.372135i \(-0.121374\pi\)
\(318\) 11.2170 0.841928i 0.629018 0.0472130i
\(319\) 15.3137i 0.857403i
\(320\) −3.32894 + 17.5761i −0.186093 + 0.982532i
\(321\) 4.58579 13.9416i 0.255954 0.778143i
\(322\) −4.65369 11.2350i −0.259340 0.626102i
\(323\) 3.06147 0.170345
\(324\) 15.9180 + 8.40333i 0.884336 + 0.466851i
\(325\) −8.50894 + 21.6569i −0.471991 + 1.20131i
\(326\) −3.25623 7.86123i −0.180346 0.435393i
\(327\) 0.798447 + 0.262632i 0.0441542 + 0.0145236i
\(328\) −22.4700 9.30739i −1.24070 0.513914i
\(329\) 8.59890i 0.474073i
\(330\) −8.60015 10.7857i −0.473422 0.593735i
\(331\) −18.4853 −1.01604 −0.508021 0.861344i \(-0.669623\pi\)
−0.508021 + 0.861344i \(0.669623\pi\)
\(332\) −13.2513 + 13.2513i −0.727262 + 0.727262i
\(333\) −4.65369 3.43289i −0.255021 0.188121i
\(334\) −9.41421 22.7279i −0.515123 1.24362i
\(335\) 6.08034 4.14386i 0.332205 0.226403i
\(336\) 21.6569 + 7.12356i 1.18148 + 0.388622i
\(337\) 27.9222i 1.52102i −0.649328 0.760508i \(-0.724950\pi\)
0.649328 0.760508i \(-0.275050\pi\)
\(338\) −11.3107 + 4.68506i −0.615222 + 0.254833i
\(339\) 4.82843 14.6792i 0.262244 0.797267i
\(340\) −16.2382 3.07554i −0.880638 0.166795i
\(341\) −2.95068 −0.159788
\(342\) 3.41157 + 0.845230i 0.184477 + 0.0457048i
\(343\) 10.4366 0.563521
\(344\) 15.7225 + 6.51246i 0.847699 + 0.351128i
\(345\) 2.80109 + 9.72524i 0.150805 + 0.523589i
\(346\) −11.6569 28.1421i −0.626676 1.51293i
\(347\) −0.185709 −0.00996939 −0.00498469 0.999988i \(-0.501587\pi\)
−0.00498469 + 0.999988i \(0.501587\pi\)
\(348\) −9.49433 18.8017i −0.508949 1.00788i
\(349\) 2.34315i 0.125426i 0.998032 + 0.0627129i \(0.0199752\pi\)
−0.998032 + 0.0627129i \(0.980025\pi\)
\(350\) 0.426486 + 23.2646i 0.0227966 + 1.24354i
\(351\) −19.7164 + 14.0000i −1.05238 + 0.747265i
\(352\) 13.1626 5.45214i 0.701571 0.290600i
\(353\) 32.3630 1.72251 0.861254 0.508175i \(-0.169680\pi\)
0.861254 + 0.508175i \(0.169680\pi\)
\(354\) −6.15188 + 0.461750i −0.326969 + 0.0245417i
\(355\) −8.97056 13.1626i −0.476108 0.698600i
\(356\) −7.12356 7.12356i −0.377548 0.377548i
\(357\) −6.58132 + 20.0083i −0.348320 + 1.05895i
\(358\) −5.21828 12.5980i −0.275795 0.665827i
\(359\) 9.21001 0.486086 0.243043 0.970016i \(-0.421854\pi\)
0.243043 + 0.970016i \(0.421854\pi\)
\(360\) −17.2460 7.91040i −0.908946 0.416914i
\(361\) −18.3137 −0.963879
\(362\) −5.59767 13.5140i −0.294207 0.710279i
\(363\) 2.52027 7.66206i 0.132280 0.402154i
\(364\) −21.6569 + 21.6569i −1.13513 + 1.13513i
\(365\) −12.1607 + 8.28772i −0.636519 + 0.433799i
\(366\) 20.7263 1.55568i 1.08338 0.0813167i
\(367\) 2.16148 0.112828 0.0564142 0.998407i \(-0.482033\pi\)
0.0564142 + 0.998407i \(0.482033\pi\)
\(368\) −10.4525 −0.544874
\(369\) 15.3137 20.7596i 0.797200 1.08070i
\(370\) 5.09920 + 3.33998i 0.265095 + 0.173638i
\(371\) 15.1114i 0.784543i
\(372\) −3.62275 + 1.82939i −0.187831 + 0.0948493i
\(373\) −24.3976 −1.26326 −0.631631 0.775269i \(-0.717614\pi\)
−0.631631 + 0.775269i \(0.717614\pi\)
\(374\) 5.03712 + 12.1607i 0.260463 + 0.628814i
\(375\) 1.81640 19.2795i 0.0937987 0.995591i
\(376\) −6.82843 2.82843i −0.352149 0.145865i
\(377\) 28.2960 1.45732
\(378\) −12.8580 + 20.4794i −0.661343 + 1.05335i
\(379\) 20.8284 1.06988 0.534942 0.844889i \(-0.320333\pi\)
0.534942 + 0.844889i \(0.320333\pi\)
\(380\) −3.64012 0.689446i −0.186734 0.0353678i
\(381\) 1.78089 5.41421i 0.0912378 0.277379i
\(382\) −6.58132 + 2.72607i −0.336729 + 0.139478i
\(383\) 29.1158i 1.48775i −0.668320 0.743874i \(-0.732986\pi\)
0.668320 0.743874i \(-0.267014\pi\)
\(384\) 12.7804 14.8547i 0.652198 0.758049i
\(385\) 15.3137 10.4366i 0.780459 0.531896i
\(386\) −10.6853 25.7967i −0.543870 1.31302i
\(387\) −10.7151 + 14.5257i −0.544681 + 0.738381i
\(388\) 3.85525 + 3.85525i 0.195720 + 0.195720i
\(389\) 7.55568 0.383088 0.191544 0.981484i \(-0.438650\pi\)
0.191544 + 0.981484i \(0.438650\pi\)
\(390\) 19.9294 15.8910i 1.00917 0.804672i
\(391\) 9.65685i 0.488368i
\(392\) −4.14386 + 10.0042i −0.209297 + 0.505286i
\(393\) −35.8728 11.7996i −1.80954 0.595211i
\(394\) 6.48528 + 15.6569i 0.326724 + 0.788781i
\(395\) 30.4608 20.7596i 1.53265 1.04453i
\(396\) 2.25576 + 14.9420i 0.113356 + 0.750866i
\(397\) −27.1237 −1.36130 −0.680650 0.732609i \(-0.738303\pi\)
−0.680650 + 0.732609i \(0.738303\pi\)
\(398\) 4.96362 + 11.9832i 0.248804 + 0.600665i
\(399\) −1.47534 + 4.48528i −0.0738593 + 0.224545i
\(400\) 18.6148 + 7.31371i 0.930739 + 0.365685i
\(401\) 15.1114i 0.754625i −0.926086 0.377313i \(-0.876848\pi\)
0.926086 0.377313i \(-0.123152\pi\)
\(402\) −8.03782 + 0.603305i −0.400890 + 0.0300901i
\(403\) 5.45214i 0.271590i
\(404\) −18.6731 + 18.6731i −0.929024 + 0.929024i
\(405\) 12.5430 15.7377i 0.623266 0.782010i
\(406\) 26.1421 10.8284i 1.29741 0.537406i
\(407\) 4.85483i 0.240645i
\(408\) 13.7239 + 11.8076i 0.679435 + 0.584562i
\(409\) −12.8284 −0.634325 −0.317162 0.948371i \(-0.602730\pi\)
−0.317162 + 0.948371i \(0.602730\pi\)
\(410\) −14.8993 + 22.7469i −0.735823 + 1.12339i
\(411\) −6.48528 + 19.7164i −0.319895 + 0.972537i
\(412\) 8.50894 8.50894i 0.419205 0.419205i
\(413\) 8.28772i 0.407812i
\(414\) 2.66613 10.7612i 0.131033 0.528884i
\(415\) 11.7996 + 17.3137i 0.579219 + 0.849897i
\(416\) 10.0742 + 24.3214i 0.493930 + 1.19245i
\(417\) 7.83938 23.8331i 0.383896 1.16711i
\(418\) 1.12918 + 2.72607i 0.0552298 + 0.133336i
\(419\) 2.51856i 0.123040i −0.998106 0.0615199i \(-0.980405\pi\)
0.998106 0.0615199i \(-0.0195948\pi\)
\(420\) 12.3312 22.3080i 0.601699 1.08852i
\(421\) 34.8284i 1.69743i −0.528848 0.848717i \(-0.677376\pi\)
0.528848 0.848717i \(-0.322624\pi\)
\(422\) −24.1522 + 10.0042i −1.17571 + 0.486995i
\(423\) 4.65369 6.30864i 0.226270 0.306737i
\(424\) 12.0000 + 4.97056i 0.582772 + 0.241392i
\(425\) −6.75699 + 17.1978i −0.327762 + 0.834216i
\(426\) 1.30603 + 17.4002i 0.0632771 + 0.843040i
\(427\) 27.9222i 1.35125i
\(428\) 11.9832 11.9832i 0.579232 0.579232i
\(429\) −19.2842 6.34315i −0.931052 0.306250i
\(430\) 10.4252 15.9162i 0.502746 0.767548i
\(431\) 27.2720 1.31365 0.656824 0.754044i \(-0.271899\pi\)
0.656824 + 0.754044i \(0.271899\pi\)
\(432\) 12.0335 + 16.9469i 0.578960 + 0.815356i
\(433\) 23.5992i 1.13410i 0.823682 + 0.567052i \(0.191916\pi\)
−0.823682 + 0.567052i \(0.808084\pi\)
\(434\) −2.08644 5.03712i −0.100152 0.241790i
\(435\) −22.6291 + 6.51770i −1.08498 + 0.312500i
\(436\) 0.686292 + 0.686292i 0.0328674 + 0.0328674i
\(437\) 2.16478i 0.103556i
\(438\) 16.0756 1.20661i 0.768124 0.0576541i
\(439\) 28.4853i 1.35953i 0.733431 + 0.679764i \(0.237918\pi\)
−0.733431 + 0.679764i \(0.762082\pi\)
\(440\) −3.25060 15.5936i −0.154966 0.743394i
\(441\) −9.24264 6.81801i −0.440126 0.324667i
\(442\) −22.4700 + 9.30739i −1.06879 + 0.442707i
\(443\) −1.60766 −0.0763821 −0.0381910 0.999270i \(-0.512160\pi\)
−0.0381910 + 0.999270i \(0.512160\pi\)
\(444\) −3.00994 5.96062i −0.142846 0.282878i
\(445\) −9.30739 + 6.34315i −0.441212 + 0.300694i
\(446\) 28.6208 11.8551i 1.35524 0.561357i
\(447\) −7.94435 + 24.1522i −0.375755 + 1.14236i
\(448\) 18.6148 + 18.6148i 0.879465 + 0.879465i
\(449\) 35.0067i 1.65207i 0.563620 + 0.826035i \(0.309408\pi\)
−0.563620 + 0.826035i \(0.690592\pi\)
\(450\) −12.2778 + 17.2990i −0.578781 + 0.815483i
\(451\) 21.6569 1.01978
\(452\) 12.6173 12.6173i 0.593467 0.593467i
\(453\) 4.65369 + 1.53073i 0.218650 + 0.0719201i
\(454\) −5.41421 + 2.24264i −0.254102 + 0.105252i
\(455\) 19.2842 + 28.2960i 0.904060 + 1.32654i
\(456\) 3.07650 + 2.64691i 0.144070 + 0.123953i
\(457\) 18.6148i 0.870762i 0.900246 + 0.435381i \(0.143386\pi\)
−0.900246 + 0.435381i \(0.856614\pi\)
\(458\) −10.4525 25.2346i −0.488413 1.17913i
\(459\) −15.6569 + 11.1175i −0.730799 + 0.518919i
\(460\) −2.17473 + 11.4821i −0.101398 + 0.535357i
\(461\) −3.99390 −0.186014 −0.0930072 0.995665i \(-0.529648\pi\)
−0.0930072 + 0.995665i \(0.529648\pi\)
\(462\) −20.2437 + 1.51946i −0.941824 + 0.0706917i
\(463\) 25.7607 1.19720 0.598600 0.801048i \(-0.295724\pi\)
0.598600 + 0.801048i \(0.295724\pi\)
\(464\) 24.3214i 1.12909i
\(465\) 1.25584 + 4.36023i 0.0582384 + 0.202201i
\(466\) −20.8284 + 8.62742i −0.964858 + 0.399657i
\(467\) −15.8645 −0.734120 −0.367060 0.930197i \(-0.619636\pi\)
−0.367060 + 0.930197i \(0.619636\pi\)
\(468\) −27.6093 + 4.16810i −1.27624 + 0.192670i
\(469\) 10.8284i 0.500010i
\(470\) −4.52775 + 6.91258i −0.208850 + 0.318853i
\(471\) −3.12967 + 9.51472i −0.144207 + 0.438415i
\(472\) −6.58132 2.72607i −0.302930 0.125478i
\(473\) −15.1535 −0.696758
\(474\) −40.2673 + 3.02239i −1.84954 + 0.138823i
\(475\) −1.51472 + 3.85525i −0.0695001 + 0.176891i
\(476\) −17.1978 + 17.1978i −0.788260 + 0.788260i
\(477\) −8.17821 + 11.0866i −0.374455 + 0.507618i
\(478\) −29.0513 + 12.0335i −1.32878 + 0.550397i
\(479\) −19.2842 −0.881120 −0.440560 0.897723i \(-0.645220\pi\)
−0.440560 + 0.897723i \(0.645220\pi\)
\(480\) −13.6588 17.1300i −0.623437 0.781873i
\(481\) 8.97056 0.409022
\(482\) 8.47343 3.50981i 0.385954 0.159867i
\(483\) 14.1480 + 4.65369i 0.643757 + 0.211750i
\(484\) 6.58579 6.58579i 0.299354 0.299354i
\(485\) 5.03712 3.43289i 0.228724 0.155879i
\(486\) −20.5167 + 8.06619i −0.930658 + 0.365890i
\(487\) 8.74280 0.396174 0.198087 0.980184i \(-0.436527\pi\)
0.198087 + 0.980184i \(0.436527\pi\)
\(488\) 22.1731 + 9.18440i 1.00373 + 0.415758i
\(489\) 9.89949 + 3.25623i 0.447671 + 0.147252i
\(490\) 10.1274 + 6.63350i 0.457511 + 0.299671i
\(491\) 36.9142i 1.66591i 0.553338 + 0.832957i \(0.313354\pi\)
−0.553338 + 0.832957i \(0.686646\pi\)
\(492\) 26.5896 13.4270i 1.19875 0.605336i
\(493\) 22.4700 1.01200
\(494\) −5.03712 + 2.08644i −0.226631 + 0.0938735i
\(495\) 16.8832 + 0.630865i 0.758845 + 0.0283553i
\(496\) −4.68629 −0.210421
\(497\) −23.4412 −1.05148
\(498\) −1.71790 22.8876i −0.0769811 1.02562i
\(499\) −37.1127 −1.66139 −0.830696 0.556726i \(-0.812057\pi\)
−0.830696 + 0.556726i \(0.812057\pi\)
\(500\) 11.9071 18.9267i 0.532502 0.846429i
\(501\) 28.6208 + 9.41421i 1.27868 + 0.420596i
\(502\) −6.34746 15.3241i −0.283301 0.683949i
\(503\) 9.63274i 0.429503i −0.976669 0.214751i \(-0.931106\pi\)
0.976669 0.214751i \(-0.0688941\pi\)
\(504\) −23.9126 + 14.4164i −1.06515 + 0.642159i
\(505\) 16.6274 + 24.3976i 0.739910 + 1.08568i
\(506\) 8.59890 3.56178i 0.382268 0.158341i
\(507\) 4.68506 14.2434i 0.208071 0.632570i
\(508\) 4.65369 4.65369i 0.206474 0.206474i
\(509\) −13.2039 −0.585253 −0.292626 0.956227i \(-0.594529\pi\)
−0.292626 + 0.956227i \(0.594529\pi\)
\(510\) 15.8260 12.6191i 0.700789 0.558784i
\(511\) 21.6569i 0.958043i
\(512\) 20.9050 8.65914i 0.923880 0.382683i
\(513\) −3.50981 + 2.49221i −0.154962 + 0.110034i
\(514\) 21.3137 8.82843i 0.940107 0.389405i
\(515\) −7.57675 11.1175i −0.333871 0.489894i
\(516\) −18.6050 + 9.39500i −0.819040 + 0.413592i
\(517\) 6.58132 0.289446
\(518\) 8.28772 3.43289i 0.364141 0.150832i
\(519\) 35.4388 + 11.6569i 1.55559 + 0.511679i
\(520\) 28.8132 6.00632i 1.26354 0.263395i
\(521\) 34.3956i 1.50690i −0.657506 0.753450i \(-0.728388\pi\)
0.657506 0.753450i \(-0.271612\pi\)
\(522\) 25.0397 + 6.20367i 1.09596 + 0.271527i
\(523\) 12.5980i 0.550874i −0.961319 0.275437i \(-0.911177\pi\)
0.961319 0.275437i \(-0.0888225\pi\)
\(524\) −30.8338 30.8338i −1.34698 1.34698i
\(525\) −21.9399 18.1872i −0.957534 0.793755i
\(526\) −12.0416 29.0711i −0.525040 1.26756i
\(527\) 4.32957i 0.188599i
\(528\) −5.45214 + 16.5754i −0.237274 + 0.721353i
\(529\) 16.1716 0.703112
\(530\) 7.95689 12.1479i 0.345625 0.527670i
\(531\) 4.48528 6.08034i 0.194645 0.263864i
\(532\) −3.85525 + 3.85525i −0.167146 + 0.167146i
\(533\) 40.0166i 1.73331i
\(534\) 12.3038 0.923499i 0.532436 0.0399637i
\(535\) −10.6704 15.6569i −0.461322 0.676905i
\(536\) −8.59890 3.56178i −0.371416 0.153846i
\(537\) 15.8645 + 5.21828i 0.684602 + 0.225185i
\(538\) −12.5980 + 5.21828i −0.543140 + 0.224976i
\(539\) 9.64212i 0.415316i
\(540\) 21.1199 9.69286i 0.908854 0.417114i
\(541\) 16.0000i 0.687894i −0.938989 0.343947i \(-0.888236\pi\)
0.938989 0.343947i \(-0.111764\pi\)
\(542\) 7.65367 + 18.4776i 0.328753 + 0.793680i
\(543\) 17.0179 + 5.59767i 0.730307 + 0.240219i
\(544\) 8.00000 + 19.3137i 0.342997 + 0.828068i
\(545\) 0.896683 0.611105i 0.0384097 0.0261769i
\(546\) −2.80760 37.4056i −0.120154 1.60081i
\(547\) 11.0011i 0.470375i 0.971950 + 0.235188i \(0.0755704\pi\)
−0.971950 + 0.235188i \(0.924430\pi\)
\(548\) −16.9469 + 16.9469i −0.723934 + 0.723934i
\(549\) −15.1114 + 20.4853i −0.644937 + 0.874291i
\(550\) −17.8059 + 0.326418i −0.759247 + 0.0139185i
\(551\) 5.03712 0.214589
\(552\) 8.34921 9.70427i 0.355366 0.413041i
\(553\) 54.2474i 2.30683i
\(554\) −19.7164 + 8.16679i −0.837668 + 0.346973i
\(555\) −7.17401 + 2.06628i −0.304520 + 0.0877085i
\(556\) 20.4853 20.4853i 0.868769 0.868769i
\(557\) 4.96362i 0.210315i 0.994456 + 0.105158i \(0.0335347\pi\)
−0.994456 + 0.105158i \(0.966465\pi\)
\(558\) 1.19534 4.82469i 0.0506026 0.204246i
\(559\) 28.0000i 1.18427i
\(560\) 24.3214 16.5754i 1.02777 0.700440i
\(561\) −15.3137 5.03712i −0.646545 0.212667i
\(562\) 1.92762 + 4.65369i 0.0813119 + 0.196304i
\(563\) −21.9874 −0.926658 −0.463329 0.886186i \(-0.653345\pi\)
−0.463329 + 0.886186i \(0.653345\pi\)
\(564\) 8.08034 4.08034i 0.340244 0.171813i
\(565\) −11.2350 16.4853i −0.472660 0.693541i
\(566\) −9.76869 23.5837i −0.410609 0.991297i
\(567\) −8.74280 28.2960i −0.367163 1.18832i
\(568\) −7.71049 + 18.6148i −0.323525 + 0.781058i
\(569\) 15.7225i 0.659120i 0.944135 + 0.329560i \(0.106900\pi\)
−0.944135 + 0.329560i \(0.893100\pi\)
\(570\) 3.54774 2.82884i 0.148598 0.118487i
\(571\) 21.1127 0.883539 0.441769 0.897129i \(-0.354351\pi\)
0.441769 + 0.897129i \(0.354351\pi\)
\(572\) −16.5754 16.5754i −0.693054 0.693054i
\(573\) 2.72607 8.28772i 0.113883 0.346224i
\(574\) 15.3137 + 36.9706i 0.639182 + 1.54312i
\(575\) 12.1607 + 4.77791i 0.507136 + 0.199253i
\(576\) 3.58261 + 23.7311i 0.149276 + 0.988796i
\(577\) 3.85525i 0.160496i −0.996775 0.0802480i \(-0.974429\pi\)
0.996775 0.0802480i \(-0.0255712\pi\)
\(578\) 4.36803 1.80930i 0.181686 0.0752569i
\(579\) 32.4853 + 10.6853i 1.35004 + 0.444068i
\(580\) −26.7171 5.06027i −1.10937 0.210116i
\(581\) 30.8338 1.27920
\(582\) −6.65875 + 0.499794i −0.276014 + 0.0207171i
\(583\) −11.5657 −0.479004
\(584\) 17.1978 + 7.12356i 0.711650 + 0.294775i
\(585\) −1.16569 + 31.1961i −0.0481952 + 1.28980i
\(586\) 1.31371 + 3.17157i 0.0542688 + 0.131016i
\(587\) 7.20533 0.297396 0.148698 0.988883i \(-0.452492\pi\)
0.148698 + 0.988883i \(0.452492\pi\)
\(588\) −5.97801 11.8383i −0.246529 0.488204i
\(589\) 0.970563i 0.0399913i
\(590\) −4.36390 + 6.66242i −0.179659 + 0.274287i
\(591\) −19.7164 6.48528i −0.811023 0.266769i
\(592\) 7.71049i 0.316899i
\(593\) 1.00547 0.0412897 0.0206448 0.999787i \(-0.493428\pi\)
0.0206448 + 0.999787i \(0.493428\pi\)
\(594\) −15.6743 9.84107i −0.643124 0.403784i
\(595\) 15.3137 + 22.4700i 0.627801 + 0.921181i
\(596\) −20.7596 + 20.7596i −0.850346 + 0.850346i
\(597\) −15.0903 4.96362i −0.617603 0.203147i
\(598\) 6.58132 + 15.8887i 0.269130 + 0.649737i
\(599\) −32.3092 −1.32012 −0.660058 0.751214i \(-0.729468\pi\)
−0.660058 + 0.751214i \(0.729468\pi\)
\(600\) −21.6592 + 11.4402i −0.884233 + 0.467046i
\(601\) 13.5147 0.551277 0.275638 0.961261i \(-0.411111\pi\)
0.275638 + 0.961261i \(0.411111\pi\)
\(602\) −10.7151 25.8686i −0.436716 1.05433i
\(603\) 5.86030 7.94435i 0.238650 0.323519i
\(604\) 4.00000 + 4.00000i 0.162758 + 0.162758i
\(605\) −5.86428 8.60474i −0.238417 0.349833i
\(606\) −2.42079 32.2521i −0.0983378 1.31015i
\(607\) −4.88755 −0.198380 −0.0991898 0.995069i \(-0.531625\pi\)
−0.0991898 + 0.995069i \(0.531625\pi\)
\(608\) 1.79337 + 4.32957i 0.0727306 + 0.175587i
\(609\) −10.8284 + 32.9203i −0.438790 + 1.33400i
\(610\) 14.7024 22.4464i 0.595283 0.908827i
\(611\) 12.1607i 0.491969i
\(612\) −21.9247 + 3.30990i −0.886252 + 0.133795i
\(613\) 23.2685 0.939804 0.469902 0.882718i \(-0.344289\pi\)
0.469902 + 0.882718i \(0.344289\pi\)
\(614\) 3.86733 + 9.33657i 0.156073 + 0.376793i
\(615\) −9.21742 32.0024i −0.371682 1.29046i
\(616\) −21.6569 8.97056i −0.872580 0.361434i
\(617\) −8.55035 −0.344224 −0.172112 0.985077i \(-0.555059\pi\)
−0.172112 + 0.985077i \(0.555059\pi\)
\(618\) 1.10310 + 14.6966i 0.0443732 + 0.591183i
\(619\) −2.48528 −0.0998919 −0.0499459 0.998752i \(-0.515905\pi\)
−0.0499459 + 0.998752i \(0.515905\pi\)
\(620\) −0.975024 + 5.14791i −0.0391579 + 0.206745i
\(621\) 7.86123 + 11.0711i 0.315460 + 0.444267i
\(622\) 44.9400 18.6148i 1.80193 0.746384i
\(623\) 16.5754i 0.664081i
\(624\) −30.6274 10.0742i −1.22608 0.403292i
\(625\) −18.3137 17.0179i −0.732548 0.680715i
\(626\) 9.21001 + 22.2349i 0.368106 + 0.888686i
\(627\) −3.43289 1.12918i −0.137096 0.0450949i
\(628\) −8.17821 + 8.17821i −0.326346 + 0.326346i
\(629\) 7.12356 0.284035
\(630\) 10.8613 + 29.2676i 0.432724 + 1.16605i
\(631\) 2.14214i 0.0852771i −0.999091 0.0426385i \(-0.986424\pi\)
0.999091 0.0426385i \(-0.0135764\pi\)
\(632\) −43.0781 17.8435i −1.71356 0.709778i
\(633\) 10.0042 30.4144i 0.397630 1.20886i
\(634\) 7.17157 + 17.3137i 0.284820 + 0.687615i
\(635\) −4.14386 6.08034i −0.164444 0.241291i
\(636\) −14.2001 + 7.17063i −0.563069 + 0.284334i
\(637\) 17.8163 0.705908
\(638\) 8.28772 + 20.0083i 0.328114 + 0.792137i
\(639\) −17.1978 12.6863i −0.680335 0.501862i
\(640\) −5.16263 24.7658i −0.204071 0.978956i
\(641\) 35.0067i 1.38268i −0.722529 0.691341i \(-0.757020\pi\)
0.722529 0.691341i \(-0.242980\pi\)
\(642\) 1.55351 + 20.6974i 0.0613121 + 0.816859i
\(643\) 35.0681i 1.38295i −0.722401 0.691475i \(-0.756961\pi\)
0.722401 0.691475i \(-0.243039\pi\)
\(644\) 12.1607 + 12.1607i 0.479198 + 0.479198i
\(645\) 6.44951 + 22.3924i 0.253949 + 0.881699i
\(646\) −4.00000 + 1.65685i −0.157378 + 0.0651881i
\(647\) 28.3730i 1.11546i 0.830024 + 0.557728i \(0.188327\pi\)
−0.830024 + 0.557728i \(0.811673\pi\)
\(648\) −25.3458 2.36469i −0.995676 0.0928938i
\(649\) 6.34315 0.248990
\(650\) −0.603142 32.9010i −0.0236572 1.29049i
\(651\) 6.34315 + 2.08644i 0.248607 + 0.0817742i
\(652\) 8.50894 + 8.50894i 0.333236 + 0.333236i
\(653\) 24.2291i 0.948158i −0.880482 0.474079i \(-0.842781\pi\)
0.880482 0.474079i \(-0.157219\pi\)
\(654\) −1.18536 + 0.0889709i −0.0463511 + 0.00347904i
\(655\) −40.2863 + 27.4558i −1.57412 + 1.07279i
\(656\) 34.3956 1.34292
\(657\) −11.7206 + 15.8887i −0.457264 + 0.619877i
\(658\) 4.65369 + 11.2350i 0.181420 + 0.437986i
\(659\) 14.6792i 0.571822i −0.958256 0.285911i \(-0.907704\pi\)
0.958256 0.285911i \(-0.0922962\pi\)
\(660\) 17.0738 + 9.43786i 0.664598 + 0.367368i
\(661\) 44.7696i 1.74133i 0.491873 + 0.870667i \(0.336312\pi\)
−0.491873 + 0.870667i \(0.663688\pi\)
\(662\) 24.1522 10.0042i 0.938701 0.388823i
\(663\) 9.30739 28.2960i 0.361469 1.09893i
\(664\) 10.1421 24.4853i 0.393591 0.950213i
\(665\) 3.43289 + 5.03712i 0.133122 + 0.195331i
\(666\) 7.93821 + 1.96672i 0.307599 + 0.0762089i
\(667\) 15.8887i 0.615213i
\(668\) 24.6005 + 24.6005i 0.951823 + 0.951823i
\(669\) −11.8551 + 36.0416i −0.458346 + 1.39345i
\(670\) −5.70171 + 8.70487i −0.220276 + 0.336299i
\(671\) −21.3707 −0.825006
\(672\) −32.1513 + 2.41322i −1.24026 + 0.0930920i
\(673\) 47.6661i 1.83739i 0.394964 + 0.918697i \(0.370757\pi\)
−0.394964 + 0.918697i \(0.629243\pi\)
\(674\) 15.1114 + 36.4821i 0.582068 + 1.40524i
\(675\) −6.25348 25.2169i −0.240696 0.970600i
\(676\) 12.2426 12.2426i 0.470871 0.470871i
\(677\) 1.00547i 0.0386433i −0.999813 0.0193217i \(-0.993849\pi\)
0.999813 0.0193217i \(-0.00615066\pi\)
\(678\) 1.63571 + 21.7925i 0.0628189 + 0.836935i
\(679\) 8.97056i 0.344259i
\(680\) 22.8807 4.76965i 0.877433 0.182908i
\(681\) 2.24264 6.81801i 0.0859382 0.261267i
\(682\) 3.85525 1.59689i 0.147625 0.0611483i
\(683\) −14.9678 −0.572726 −0.286363 0.958121i \(-0.592446\pi\)
−0.286363 + 0.958121i \(0.592446\pi\)
\(684\) −4.91487 + 0.741983i −0.187925 + 0.0283704i
\(685\) 15.0903 + 22.1421i 0.576569 + 0.846008i
\(686\) −13.6360 + 5.64823i −0.520626 + 0.215650i
\(687\) 31.7774 + 10.4525i 1.21238 + 0.398788i
\(688\) −24.0669 −0.917542
\(689\) 21.3707i 0.814159i
\(690\) −8.92306 11.1907i −0.339695 0.426023i
\(691\) −7.17157 −0.272819 −0.136410 0.990653i \(-0.543556\pi\)
−0.136410 + 0.990653i \(0.543556\pi\)
\(692\) 30.4608 + 30.4608i 1.15795 + 1.15795i
\(693\) 14.7595 20.0083i 0.560668 0.760053i
\(694\) 0.242641 0.100505i 0.00921051 0.00381512i
\(695\) −18.2410 26.7653i −0.691922 1.01527i
\(696\) 22.5804 + 19.4273i 0.855906 + 0.736391i
\(697\) 31.7774i 1.20365i
\(698\) −1.26810 3.06147i −0.0479983 0.115878i
\(699\) 8.62742 26.2288i 0.326319 0.992065i
\(700\) −13.1479 30.1658i −0.496945 1.14016i
\(701\) −26.8399 −1.01373 −0.506865 0.862025i \(-0.669196\pi\)
−0.506865 + 0.862025i \(0.669196\pi\)
\(702\) 18.1839 28.9623i 0.686308 1.09311i
\(703\) 1.59689 0.0602280
\(704\) −14.2471 + 14.2471i −0.536959 + 0.536959i
\(705\) −2.80109 9.72524i −0.105495 0.366274i
\(706\) −42.2843 + 17.5147i −1.59139 + 0.659175i
\(707\) 43.4495 1.63409
\(708\) 7.78793 3.93268i 0.292688 0.147799i
\(709\) 36.2843i 1.36268i −0.731965 0.681342i \(-0.761397\pi\)
0.731965 0.681342i \(-0.238603\pi\)
\(710\) 18.8442 + 12.3430i 0.707209 + 0.463223i
\(711\) 29.3585 39.7990i 1.10103 1.49258i
\(712\) 13.1626 + 5.45214i 0.493290 + 0.204328i
\(713\) −3.06147 −0.114653
\(714\) −2.22952 29.7039i −0.0834379 1.11164i
\(715\) −21.6569 + 14.7595i −0.809920 + 0.551975i
\(716\) 13.6360 + 13.6360i 0.509602 + 0.509602i
\(717\) 12.0335 36.5838i 0.449398 1.36625i
\(718\) −12.0335 + 4.98442i −0.449085 + 0.186017i
\(719\) 2.95068 0.110042 0.0550208 0.998485i \(-0.482477\pi\)
0.0550208 + 0.998485i \(0.482477\pi\)
\(720\) 26.8141 + 1.00195i 0.999303 + 0.0373403i
\(721\) −19.7990 −0.737353
\(722\) 23.9280 9.91131i 0.890508 0.368861i
\(723\) −3.50981 + 10.6704i −0.130531 + 0.396837i
\(724\) 14.6274 + 14.6274i 0.543624 + 0.543624i
\(725\) −11.1175 + 28.2960i −0.412892 + 1.05089i
\(726\) 0.853782 + 11.3749i 0.0316868 + 0.422163i
\(727\) −47.1015 −1.74690 −0.873449 0.486915i \(-0.838122\pi\)
−0.873449 + 0.486915i \(0.838122\pi\)
\(728\) 16.5754 40.0166i 0.614327 1.48312i
\(729\) 8.89949 25.4912i 0.329611 0.944117i
\(730\) 11.4034 17.4097i 0.422059 0.644363i
\(731\) 22.2349i 0.822388i
\(732\) −26.2383 + 13.2496i −0.969795 + 0.489719i
\(733\) 9.63811 0.355992 0.177996 0.984031i \(-0.443039\pi\)
0.177996 + 0.984031i \(0.443039\pi\)
\(734\) −2.82411 + 1.16979i −0.104240 + 0.0431776i
\(735\) −14.2482 + 4.10381i −0.525553 + 0.151371i
\(736\) 13.6569 5.65685i 0.503398 0.208514i
\(737\) 8.28772 0.305282
\(738\) −8.77332 + 35.4114i −0.322950 + 1.30351i
\(739\) −27.1716 −0.999522 −0.499761 0.866163i \(-0.666579\pi\)
−0.499761 + 0.866163i \(0.666579\pi\)
\(740\) −8.47001 1.60423i −0.311364 0.0589728i
\(741\) 2.08644 6.34315i 0.0766474 0.233021i
\(742\) −8.17821 19.7439i −0.300232 0.724823i
\(743\) 15.2304i 0.558750i 0.960182 + 0.279375i \(0.0901272\pi\)
−0.960182 + 0.279375i \(0.909873\pi\)
\(744\) 3.74330 4.35083i 0.137236 0.159509i
\(745\) 18.4853 + 27.1237i 0.677248 + 0.993736i
\(746\) 31.8771 13.2039i 1.16710 0.483429i
\(747\) 22.6215 + 16.6871i 0.827676 + 0.610551i
\(748\) −13.1626 13.1626i −0.481273 0.481273i
\(749\) −27.8832 −1.01883
\(750\) 8.06076 + 26.1730i 0.294338 + 0.955702i
\(751\) 35.1127i 1.28128i 0.767841 + 0.640640i \(0.221331\pi\)
−0.767841 + 0.640640i \(0.778669\pi\)
\(752\) 10.4525 0.381164
\(753\) 19.2974 + 6.34746i 0.703235 + 0.231314i
\(754\) −36.9706 + 15.3137i −1.34639 + 0.557692i
\(755\) 5.22625 3.56178i 0.190203 0.129627i
\(756\) 5.71637 33.7164i 0.207902 1.22625i
\(757\) 12.8319 0.466383 0.233192 0.972431i \(-0.425083\pi\)
0.233192 + 0.972431i \(0.425083\pi\)
\(758\) −27.2137 + 11.2723i −0.988444 + 0.409427i
\(759\) −3.56178 + 10.8284i −0.129284 + 0.393047i
\(760\) 5.12918 1.06922i 0.186055 0.0387845i
\(761\) 17.1978i 0.623420i 0.950177 + 0.311710i \(0.100902\pi\)
−0.950177 + 0.311710i \(0.899098\pi\)
\(762\) 0.603305 + 8.03782i 0.0218554 + 0.291180i
\(763\) 1.59689i 0.0578115i
\(764\) 7.12356 7.12356i 0.257722 0.257722i
\(765\) −0.925677 + 24.7730i −0.0334679 + 0.895670i
\(766\) 15.7574 + 38.0416i 0.569337 + 1.37450i
\(767\) 11.7206i 0.423207i
\(768\) −8.65914 + 26.3253i −0.312460 + 0.949931i
\(769\) −49.5980 −1.78855 −0.894274 0.447519i \(-0.852308\pi\)
−0.894274 + 0.447519i \(0.852308\pi\)
\(770\) −14.3601 + 21.9237i −0.517502 + 0.790077i
\(771\) −8.82843 + 26.8399i −0.317948 + 0.966616i
\(772\) 27.9222 + 27.9222i 1.00494 + 1.00494i
\(773\) 18.8490i 0.677952i −0.940795 0.338976i \(-0.889919\pi\)
0.940795 0.338976i \(-0.110081\pi\)
\(774\) 6.13877 24.7777i 0.220653 0.890616i